Boris Johnson last night questioned the political neutrality of Transport for London, claiming its statistics are being used as "attack weapons" on behalf London mayor Ken Livingstone.

In an outspoken attack on the public transport operator, the Conservative mayoral candidate said that there were "serious flaws" with some of TfL's figures and accusing it of being "highly mischievous".

"Transport for London should not be a political organisation and we would question how appropriate it is for them to be producing figures that are being used as political attack weapons," Johnson's office said in a statement.

TfL rejected the suggestion and Livingstone's campaign team hit back, accusing Johnson of "lacking in competence".

The dispute - over the cost of bus conductors - began last Wednesday after Johnson told BBC Radio London's Vanessa Feltz that he planned to introduce a new generation of Routemaster buses that would be equipped with conductors.

"It would cost eight million quid to have conductors on each of those buses, per year," he said.

The following day Livingstone, who chairs the TfL board, argued on the same programme that the figure for conductors would be nearer £80m.

His campaign website later put this at £70m but went on to claim that the total cost of introducing a new-style Routemaster fleet would be £110m.

Johnson has said that, under his administration, the new fleet would replace Livingstone's controversial "bendy buses".

And at the launch of his transport manifesto on Monday, Johnson confirmed he was standing by his £8m figure for conductors.

After both sides had provided their calculations theguardian.com asked TfL for the information necessary to make its own judgment of Johnson's plan.

TfL provided estimated costs for putting this fully into effect. The figures were largely in line with the Livingstone campaign's assessment of the new Routemaster plan and sharply at odds with Johnson's regarding conductors.

TfL put this at £49m – more than six times Johnson's figure - if existing passenger capacity on London's twelve "bendy bus" routes was to be maintained.

It also estimated that the total cost would be £112m a year. It said that this would mean roughly a 15% rise in bus fares on all routes. The Livingstone team puts it at between 15% and 20%.

Transport for London rejected the implication of political bias levelled by Johnson's camp.

A TfL spokesman said: "As one of the world's largest transport authorities, we are regularly asked for information by a whole range of people.

"In this case, a journalist asked us to provide our estimate of these costs given that we operate the bus network in London.

"This is what we have done, based on our detailed knowledge of the current system."

Invited to respond to TfL's figures, Johnson's team issued a statement reasserting that its £8m figure for conductors was correct, saying that there were "serious flaws" with TfL's analysis.

The suggestion that a body described on the Greater London Authority website as "accountable to the mayor and responsible for delivering the mayor's transport strategy" had in effect been engaged in advancing his political strategy, too, is consistent with criticisms that, under Livingstone, mayoral aides and other elements of the mayoral apparatus have crossed a similar line.

The discrepancy

The discrepancy between TfL's calculation and Johnson's arises from different methods of calculation.

Using information provided by the mayor to the London assembly, Johnson'scampaign had deduced that the wage presently paid to conductors working on the only two remaining Routemaster routes – known as "heritage routes" - is £24,600 a year and multiplied this by 337, this being the number of bendy buses operating in London according, they say, to Ken Livingstone's own figures. This produced a total of £8,290,000.

However, TfL pointed out that very few of the old Routemasters work the two "heritage" routes: four an hour and between 9.30am and 6.30pm only.

By comparison, the bendy buses operate high frequency services on some of the capital's busiest routes, of which a number work right through the night. They said that there are 399 bendy buses, of which a maximum of 350 are required to be on the roads at any one time. To staff them takes, according to TfL, "roughly three drivers per bus to work a 20 hour day, seven days a week". The number of conductors would have to be the same.

TfL also emphasised that bendy buses can carry more passengers – up to 149 - than a modern double-decker's 90 and the old Routemaster's maximum of 69.

Its view was that, if it was assumed that any new Routemaster could carry as many passengers as a modern double-decker, 620 such buses would be needed to replace the 399 bendy buses, with a maximum of 560 being out on the road at the same time.

Such an enlarged fleet would mean taking on still more conductors as well as additional drivers. TfL estimated that a total of 1,736 conductors would have to be hired at around £28,000 per year if add-ons such as national insurance and pensions were included, together with an extra 651 drivers at £35,000 per year making staffing a new Routemaster fleet cost at least £72m more than the present fleet of bendy buses.

It also theorised that the cost of new buses would be £40m a year, meaning that Johnson's scheme would coast £112m in all.

All these estimates are sharply disputed by the Johnson team, which emphases that its policy envisages a competition for designing a new Routemaster, rendering any projections based on the capacities of existing buses and contracts with bus companies meaningless.

It adds that, in any case, they wouldn't "purge 330-odd bendy buses in one swoop" and that their replacements would be introduced over time. They anticipate great interest from bus manufacturers.

The discrepancy between the Livingstone camp's latest estimate of the cost of conductors and that of TfL is explained by the former using a much higher figure for the cost of each one. They put this at £40,000 - £25,000 plus "add-ons" that might also include the cost of training and providing uniforms.

A spokesman for the Livingstone campaign thought the TfL figure of £28,000 "seems low" but asserted that the TfL figures "have to be taken as definitive" and showed "our analysis is fundamentally correct" and Johnson's to be "completely ridiculous".